Linear Programming: Foundations and Extensions / Edition 1

by Robert J. Vanderbei

Overview

This book focuses largely on constrained optimization. It begins with a substantial treatment of linear programming and proceeds to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Along the way, dynamic programming and the linear complementarity problem are touched on as well.
This book aims to be the first introduction to the topic. Specific examples and concrete algorithms precede more abstract topics. Nevertheless, topics covered are developed in some depth, a large number of numerical examples worked out in detail, and many recent results are included, most notably interior-point methods. The exercises at the end of each chapter both illustrate the theory, and, in some cases, extend it.
Optimization is not merely an intellectual exercise: its purpose is to solve practical problems on a computer. Accordingly, the book comes with software that implements the major algorithms studied. At this point, software for the following four algorithms is available:
• The two-phase simplex method
• The primal-dual simplex method
• The path-following interior-point method
• The homogeneous self-dual methods.£/LIST£.

Product Details

ISBN-13:	9780792381419
Publisher:	Springer US
Publication date:	03/31/1998
Series:	International Series in Operations Research & Management Science , #4
Edition description:	1997
Pages:	418
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

Robert J. Vanderbei is Professor of Operations Research and Financial Engineering, and former Department Chair, OR and Financial Engineering at Princeton University. His research interests are in algorithms for nonlinear optimization and their application to problems arising in engineering and science. Application areas of interest focus mainly on inverse Fourier transform optimization problems and action minimization problems with a special interest in applying these techniques to the design of NASA’s terrestrial planet finder space telescope.

Table of Contents

Chapter 1. Introduction.- Chapter 2. The Simplex Method.- Chapter 3. Degeneracy.- Chapter 4. Efficiency of the Simplex Method.- Chapter 5. Duality Theory.- Chapter 6. The Simplex Method in Matrix Notational.- Chapter 7. Sensitivity and Parametric Analyses.- Chapter 8. Implementation Issues.- Chapter 9. Problems in General Form.- Chapter 10. Convex Analysis.- Chapter 11. Game Theory.- Chapter 12. Data Science Applications.- Chapter 13. Financial Applications.- Chapter 14. Network Flow Problems.- Chapter 15. Applications.- Chapter 16. Structural Optimization.- Chapter 17. The Central Path.- Chapter 18. A Path-Following Method.- Chapter 19. The KKT System.- Chapter 20. Implementation Issues.- Chapter 21. The Affine-Scaling Method.- Chapter 22. The Homogeneous Self-Dual Method.- Chapter 23. Integer Programming.- Chapter 24. Quadratic Programming.- Chapter 25. Convex Programming.

Editorial Reviews

Constrained optimization is introduced here with specific examples and concrete algorithms preceding more abstract topics. The book begins with treatment of linear programming, then proceeds to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Dynamic programming and the linear complementarity problem are covered as well. Early chapters assume background only in linear algebra. Later chapters require some knowledge of multivariate calculus. Code is included for C programs that implement example algorithms. This second edition adds many new exercises, and offers online tools for learning the simplex method and duality theory. Vanderbei is affiliated with the Department of Operations Research & Financial Engineering at Princeton University. Annotation c. Book News, Inc., Portland, OR (booknews.com)

‘Vanderbei's book is thoroughly modern. Vanderbei's book has many novel features. Some nice features. This book has style. Overall, I greatly enjoyed reviewing this book, and I highly recommend it as a textbook for an advanced undergraduate or master's level course in linear programming, particularly for courses in an engineering environment. In addition, it also is a good reference book for interior point methods as well as for implementation and computational aspects of linear programming. This is an excellent new book.'
Robert Freund, (MIT) in Optima, 56 (1997)
‘In conclusion, Vanderbei's book gives an excellent introduction to linear programminbg, especially the algorithmic side of the subject. The book is highly recommended for both self study and as teaching material.'
Optima, 58 (1998)

From the Publisher